What is the Greatest Common Factor of 31200 and 31217?

Greatest common factor (GCF) of 31200 and 31217 is 1.

GCF(31200,31217) = 1

We will now calculate the prime factors of 31200 and 31217, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31200 and 31217.

How to find the GCF of 31200 and 31217?

We will first find the prime factorization of 31200 and 31217. After we will calculate the factors of 31200 and 31217 and find the biggest common factor number .

Step-1: Prime Factorization of 31200

Prime factors of 31200 are 2, 3, 5, 13. Prime factorization of 31200 in exponential form is:

31200 = 2⁵ × 3¹ × 5² × 13¹

Step-2: Prime Factorization of 31217

Prime factors of 31217 are 19, 31, 53. Prime factorization of 31217 in exponential form is:

31217 = 19¹ × 31¹ × 53¹

Step-3: Factors of 31200

List of positive integer factors of 31200 that divides 31200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 25, 26, 30, 32, 39, 40, 48, 50, 52, 60, 65, 75, 78, 80, 96, 100, 104, 120, 130, 150, 156, 160, 195, 200, 208, 240, 260, 300, 312, 325, 390, 400, 416, 480, 520, 600, 624, 650, 780, 800, 975, 1040, 1200, 1248, 1300, 1560, 1950, 2080, 2400, 2600, 3120, 3900, 5200, 6240, 7800, 10400, 15600

Step-4: Factors of 31217

List of positive integer factors of 31217 that divides 31200 without a remainder.

1, 19, 31, 53, 589, 1007, 1643

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31200 and 31217. The biggest common factor number is the GCF number.
So the greatest common factor 31200 and 31217 is 1.

Also check out the Least Common Multiple of 31200 and 31217